Factual error: Lucas is wearing a pair of jeans with a large "W" stitched on the right back pocket. These are Wrangler jeans, which first went on sale in 1947. "The Rifleman" is set in the 1880s.
Continuity mistake: During most of the show Billy is wearing a shirt and vest. When he starts to go outside to face his ex partner it shows him wearing the vest. When he stands up to go outside he has coat on. When he gets outside he's back in the vest.